Higher-order interference and single-system postulates characterizing quantum theory

We present a new characterization of quantum theory in terms of simple physical principles that is different from previous ones in two important respects: first, it only refers to properties of single systems without any assumptions on the composition of many systems; and second, it is closer to experiment by having absence of higher-order interference as a postulate, which is currently the subject of experimental investigation. We give three postulates -- no higher-order interference, classical decomposability of states, and strong symmetry -- and prove that the only non-classical operational probabilistic theories satisfying them are real, complex, and quaternionic quantum theory, together with 3-level octonionic quantum theory and ball state spaces of arbitrary dimension. Then we show that adding observability of energy as a fourth postulate yields complex quantum theory as the unique solution, relating the emergence of the complex numbers to the possibility of Hamiltonian dynamics. We also show that there may be interesting non-quantum theories satisfying only the first two of our postulates, which would allow for higher-order interference in experiments while still respecting the contextuality analogue of the local orthogonality principle.Comment: 21 + 6 pages, 1 figure. v4: published version (includes several minor corrections

Understanding quantum mechanics: a review and synthesis in precise language

This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit

Roadmap on structured light

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.Peer ReviewedPostprint (published version

A Process Model of Non-Relativistic Quantum Mechanics

A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time and continuous wave function arise through a uniform interpolation process. Standard non-relativistic quantum mechanics (at least for integer spin particles) emerges under the limit of infinite information (the causal space grows to infinity) and infinitesimal scale (the separation between points goes to zero). This model is quasi-local, discontinuous, and quasi-non-contextual. The bridge between process and wave function is through the process covering map, which reveals that the standard wave function formalism lacks important dynamical information related to the generation of the causal space. Reformulating several classical conundrums such as wave particle duality, Schrodinger's cat, hidden variable results, the model offers potential resolutions to all, while retaining a high degree of locality and contextuality at the local level, yet nonlocality and contextuality at the emergent level. The model remains computationally powerful

Roadmap on structured light

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized